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Simplicial systems for interval exchange maps and measured foliations

Published online by Cambridge University Press:  19 September 2008

S. P. Kerckhoff
S. P. Kerckhoff
Affiliation:
School of Mathematics, The Institute for Advanced Study, Princeton, New Jersey 08540, USA
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Abstract

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The spaces of interval exchange maps and measured foliations are considered and an alternative proof that almost all interval exchange maps and measured foliations are uniquely ergodic is given. These spaces are endowed with a refinement process, called a simplicial system, which is studied abstractly and is shown to be normal under a simple assumption. The results follow and thus are a corollary of a more general theorem in a broader setting.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 5 , Issue 2 , June 1985 , pp. 257 - 271
Copyright
Copyright © Cambridge University Press 1985

References

REFERENCES

[1]Hajian, A. & Kakutani, S.. Weakly wandering sets and invariant measures. Trans. Amer. Math. Soc. 110 (1964), 136–151.Google Scholar
[2]Keane, M.. Non-ergodic interval exchange transformations. Israel J. Math. 26 (1977), 188–196.Google Scholar
[3]Kerckhoff, S. P.. The asymptotic geometry of Teichmüller space. Topology 19 (1980), 23–41.CrossRefGoogle Scholar
[4]Keynes, H. B. & Newton, D.. A minimal, non-uniquely ergodic interval exchange transformation. Math. Z. 148 (1976), 101–105.Google Scholar
[5]Masur, H.. Interval exchange transformations and measured foliations. Ann. Math. 115 (1982), 169–200.Google Scholar
[6]Rauzy, G.. Echanges d'intervalles et transformations induites. Acta Arith. 34 (1979), 315–328.CrossRefGoogle Scholar
[7]Rees, M.. An alternative approach to the ergodic theory of measured foliations on surfaces. Ergod. Th. & Dynam. Sys. 1 (1981), 461–488.Google Scholar
[8]Thurston, W. P.. The Geometry and Topology of Three-Manifolds, Chapter 9. Princeton Univ. notes.Google Scholar
[9]Thurston, W. P.. On the geometry and dynamics of diffeomorphisms of surfaces. Preprint.Google Scholar
[10]Veech, W.. Interval exchange transformations. J. Analyse Math. 33 (1978), 222–272.Google Scholar
[11]Veech, W.. Projective Swiss cheeses and uniquely ergodic interval exchange transformations. In Progress in Mathematics, Vol. I. Birkhauser: Boston (1981), (pp 113–193).Google Scholar
[12]Veech, W.. Gauss measures for transformations on the space of interval exchange maps. Ann. Math. 115 (1982), 201–242.CrossRefGoogle Scholar